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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 11:42:14 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/26/t12592610260wj70e2gvxfudrk.htm/, Retrieved Sun, 28 Apr 2024 23:54:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60263, Retrieved Sun, 28 Apr 2024 23:54:09 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2009-11-26 18:42:14] [9f6463b67b1eb7bae5c03a796abf0348] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60263&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60263&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60263&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.812974	6.2973	0
2	0.475802	3.6855	0.000246
3	0.071849	0.5565	0.289955
4	-0.318636	-2.4681	0.008225
5	-0.589462	-4.566	1.3e-05
6	-0.689815	-5.3433	1e-06
7	-0.583599	-4.5205	1.5e-05
8	-0.334592	-2.5917	0.005987
9	0.017076	0.1323	0.447606
10	0.355899	2.7568	0.003861
11	0.587635	4.5518	1.3e-05
12	0.659697	5.11	2e-06
13	0.535908	4.1511	5.3e-05
14	0.283026	2.1923	0.016124
15	-0.01726	-0.1337	0.447044
16	-0.305615	-2.3673	0.010581
17	-0.489856	-3.7944	0.000173

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.812974 & 6.2973 & 0 \tabularnewline
2 & 0.475802 & 3.6855 & 0.000246 \tabularnewline
3 & 0.071849 & 0.5565 & 0.289955 \tabularnewline
4 & -0.318636 & -2.4681 & 0.008225 \tabularnewline
5 & -0.589462 & -4.566 & 1.3e-05 \tabularnewline
6 & -0.689815 & -5.3433 & 1e-06 \tabularnewline
7 & -0.583599 & -4.5205 & 1.5e-05 \tabularnewline
8 & -0.334592 & -2.5917 & 0.005987 \tabularnewline
9 & 0.017076 & 0.1323 & 0.447606 \tabularnewline
10 & 0.355899 & 2.7568 & 0.003861 \tabularnewline
11 & 0.587635 & 4.5518 & 1.3e-05 \tabularnewline
12 & 0.659697 & 5.11 & 2e-06 \tabularnewline
13 & 0.535908 & 4.1511 & 5.3e-05 \tabularnewline
14 & 0.283026 & 2.1923 & 0.016124 \tabularnewline
15 & -0.01726 & -0.1337 & 0.447044 \tabularnewline
16 & -0.305615 & -2.3673 & 0.010581 \tabularnewline
17 & -0.489856 & -3.7944 & 0.000173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60263&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.812974[/C][C]6.2973[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.475802[/C][C]3.6855[/C][C]0.000246[/C][/ROW]
[ROW][C]3[/C][C]0.071849[/C][C]0.5565[/C][C]0.289955[/C][/ROW]
[ROW][C]4[/C][C]-0.318636[/C][C]-2.4681[/C][C]0.008225[/C][/ROW]
[ROW][C]5[/C][C]-0.589462[/C][C]-4.566[/C][C]1.3e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.689815[/C][C]-5.3433[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.583599[/C][C]-4.5205[/C][C]1.5e-05[/C][/ROW]
[ROW][C]8[/C][C]-0.334592[/C][C]-2.5917[/C][C]0.005987[/C][/ROW]
[ROW][C]9[/C][C]0.017076[/C][C]0.1323[/C][C]0.447606[/C][/ROW]
[ROW][C]10[/C][C]0.355899[/C][C]2.7568[/C][C]0.003861[/C][/ROW]
[ROW][C]11[/C][C]0.587635[/C][C]4.5518[/C][C]1.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.659697[/C][C]5.11[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.535908[/C][C]4.1511[/C][C]5.3e-05[/C][/ROW]
[ROW][C]14[/C][C]0.283026[/C][C]2.1923[/C][C]0.016124[/C][/ROW]
[ROW][C]15[/C][C]-0.01726[/C][C]-0.1337[/C][C]0.447044[/C][/ROW]
[ROW][C]16[/C][C]-0.305615[/C][C]-2.3673[/C][C]0.010581[/C][/ROW]
[ROW][C]17[/C][C]-0.489856[/C][C]-3.7944[/C][C]0.000173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60263&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60263&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.812974	6.2973	0
2	0.475802	3.6855	0.000246
3	0.071849	0.5565	0.289955
4	-0.318636	-2.4681	0.008225
5	-0.589462	-4.566	1.3e-05
6	-0.689815	-5.3433	1e-06
7	-0.583599	-4.5205	1.5e-05
8	-0.334592	-2.5917	0.005987
9	0.017076	0.1323	0.447606
10	0.355899	2.7568	0.003861
11	0.587635	4.5518	1.3e-05
12	0.659697	5.11	2e-06
13	0.535908	4.1511	5.3e-05
14	0.283026	2.1923	0.016124
15	-0.01726	-0.1337	0.447044
16	-0.305615	-2.3673	0.010581
17	-0.489856	-3.7944	0.000173

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.812974	6.2973	0
2	-0.545978	-4.2291	4.1e-05
3	-0.345765	-2.6783	0.004767
4	-0.292397	-2.2649	0.013572
5	-0.090663	-0.7023	0.242613
6	-0.041252	-0.3195	0.375214
7	0.152036	1.1777	0.12179
8	0.028404	0.22	0.413301
9	0.227675	1.7636	0.041448
10	0.065058	0.5039	0.308077
11	0.048677	0.3771	0.353732
12	-0.005439	-0.0421	0.483267
13	-0.112255	-0.8695	0.194013
14	0.00478	0.037	0.485292
15	0.095402	0.739	0.231401
16	-0.05533	-0.4286	0.33488
17	0.060116	0.4657	0.321573

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.812974 & 6.2973 & 0 \tabularnewline
2 & -0.545978 & -4.2291 & 4.1e-05 \tabularnewline
3 & -0.345765 & -2.6783 & 0.004767 \tabularnewline
4 & -0.292397 & -2.2649 & 0.013572 \tabularnewline
5 & -0.090663 & -0.7023 & 0.242613 \tabularnewline
6 & -0.041252 & -0.3195 & 0.375214 \tabularnewline
7 & 0.152036 & 1.1777 & 0.12179 \tabularnewline
8 & 0.028404 & 0.22 & 0.413301 \tabularnewline
9 & 0.227675 & 1.7636 & 0.041448 \tabularnewline
10 & 0.065058 & 0.5039 & 0.308077 \tabularnewline
11 & 0.048677 & 0.3771 & 0.353732 \tabularnewline
12 & -0.005439 & -0.0421 & 0.483267 \tabularnewline
13 & -0.112255 & -0.8695 & 0.194013 \tabularnewline
14 & 0.00478 & 0.037 & 0.485292 \tabularnewline
15 & 0.095402 & 0.739 & 0.231401 \tabularnewline
16 & -0.05533 & -0.4286 & 0.33488 \tabularnewline
17 & 0.060116 & 0.4657 & 0.321573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60263&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.812974[/C][C]6.2973[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.545978[/C][C]-4.2291[/C][C]4.1e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.345765[/C][C]-2.6783[/C][C]0.004767[/C][/ROW]
[ROW][C]4[/C][C]-0.292397[/C][C]-2.2649[/C][C]0.013572[/C][/ROW]
[ROW][C]5[/C][C]-0.090663[/C][C]-0.7023[/C][C]0.242613[/C][/ROW]
[ROW][C]6[/C][C]-0.041252[/C][C]-0.3195[/C][C]0.375214[/C][/ROW]
[ROW][C]7[/C][C]0.152036[/C][C]1.1777[/C][C]0.12179[/C][/ROW]
[ROW][C]8[/C][C]0.028404[/C][C]0.22[/C][C]0.413301[/C][/ROW]
[ROW][C]9[/C][C]0.227675[/C][C]1.7636[/C][C]0.041448[/C][/ROW]
[ROW][C]10[/C][C]0.065058[/C][C]0.5039[/C][C]0.308077[/C][/ROW]
[ROW][C]11[/C][C]0.048677[/C][C]0.3771[/C][C]0.353732[/C][/ROW]
[ROW][C]12[/C][C]-0.005439[/C][C]-0.0421[/C][C]0.483267[/C][/ROW]
[ROW][C]13[/C][C]-0.112255[/C][C]-0.8695[/C][C]0.194013[/C][/ROW]
[ROW][C]14[/C][C]0.00478[/C][C]0.037[/C][C]0.485292[/C][/ROW]
[ROW][C]15[/C][C]0.095402[/C][C]0.739[/C][C]0.231401[/C][/ROW]
[ROW][C]16[/C][C]-0.05533[/C][C]-0.4286[/C][C]0.33488[/C][/ROW]
[ROW][C]17[/C][C]0.060116[/C][C]0.4657[/C][C]0.321573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60263&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60263&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.812974	6.2973	0
2	-0.545978	-4.2291	4.1e-05
3	-0.345765	-2.6783	0.004767
4	-0.292397	-2.2649	0.013572
5	-0.090663	-0.7023	0.242613
6	-0.041252	-0.3195	0.375214
7	0.152036	1.1777	0.12179
8	0.028404	0.22	0.413301
9	0.227675	1.7636	0.041448
10	0.065058	0.5039	0.308077
11	0.048677	0.3771	0.353732
12	-0.005439	-0.0421	0.483267
13	-0.112255	-0.8695	0.194013
14	0.00478	0.037	0.485292
15	0.095402	0.739	0.231401
16	-0.05533	-0.4286	0.33488
17	0.060116	0.4657	0.321573

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code